You probably weren't aware that oak has a high concentration of tannin, and when you add tannin to water it gives you tannic acid, a weak acid which reacts with iron to create a non-black oxide. This is the stain you can see on some oak worktops, especially where folk insist on using fancy cast iron pans (and leaving them on the oak when wet....).
I'm no chemist, but I recall from school than acetic acid mixed with an alkali such as baking soda will form another acid, carbonic acid together with sodium acetate, before deteriorating into hydrogen and carbon dioxide. This can be near explosive and is the well known pop bottle rocket "experiment" so beloved of kids. I therefore suspect the carbonic acid has reacted with the tannin to produce the stain that's given you the brown, or maybe there has been some iron contamination as well? Surplus baking soda has possiply ended up blocking the open pores of the unsealed timber (even if it was oiled, the pores would still be open) as well as absorbing the brown oxide. But that is conjecture
Getting it out? I'd start by scrubbing/brushing with a medium/soft nylon brush whilst wetting with distilled or ionized water. This may take several goes as the baking soda doesn't dissolve that easily in water. It will raise the grain as well, so at the end when the top is thoroughly dry you will need to sand it back to cut the raised grain. If there is still staining it may be necessary to bleach the affected area and for that the best approach is to use oxallic acid which acts as a bleach on oak.
